Question

which equation describes the line with slope ⅔ that passes through the given point on the graph? y = ⅔x + 1 y = ⅔x - 2 y = ⅔x + ⅔ y = ⅔x + ¾

Explanation:

Step1: Recall slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We are given $m=\frac{2}{3}$.

Step2: Identify the y - intercept

We need to find the equation of the line with slope $\frac{2}{3}$ passing through a point. Since the line passes through the point $(0, 1)$ (the y - intercept is the value of $y$ when $x = 0$), substituting $m=\frac{2}{3}$ and $b = 1$ into $y=mx + b$, we get $y=\frac{2}{3}x+1$.

Answer:

$y=\frac{2}{3}x + 1$